1. Field of the Invention
The present invention relates to estimating a velocity of a geological layer, and in particular, relates to estimating Dix interval velocities based on RMS velocity data.
2. Description of Background Art
A number of techniques for exploring the Earth's subsurface have been developed that are based on transmitting waves or signals into a region of the Earth's subsurface. The transmitted signal interacts with the earth and typically a portion of the signal propagates back to the surface where it is recorded and used to obtain information about the subsurface structure, based on how the signal has interacted with the earth. Such techniques typically involve recording amplitudes and travel times of the returned signal.
In seismic imaging applications, seismic waves are transmitted into the earth and may be reflected back, e.g., from subsurface layer interfaces or horizons. Amplitudes of the reflected waves are measured and recorded as seismic time series data. Strong reflections may occur for example at subsurface layer interfaces across which there is a strong contrast in the elastic properties of the layer medium. Prominent reflection events are observed in the time series data that correspond to the strongly reflecting horizons or interfaces. Time series from different horizontal locations may then be processed to align corresponding events and to form an image where the amplitude events can be associated with structural features of the subsurface, for example, in the form of a “seismic section”. In this way, a subsurface image of the Earth's subsurface can be formed. However, raw unprocessed time-series data are often hard to interpret and such data therefore typically undergo several further processing steps in order to produce a more representative image of the subsurface.
A problem with raw or initial time series data early in the processing sequence is that the geometric features of the subsurface reflectors are often not accurately represented in the data. For example, the travel times of the time series data may not provide an accurate, correct to scale, indication of the depth of different reflectors and geological structures. This is problematic because accurate geometrical representation is necessary for example for determining where to drill or otherwise assessing a hydrocarbon prospect.
However, since seismic wave propagation is dependent on the seismic velocity of the layer through which it propagates, determination of the seismic velocity of the layers can be used to convert the recorded travel times to distance in terms of depth or as a corrected time.
In order to make an appropriate correction to the seismic reflection data for such purposes, it is desirable to find an accurate and as far as possible a “correct” model of interval seismic velocities of different layers. The interval velocity provides the link to convert the seismic data from the pre-existing time coordinate into a corrected time or depth coordinate system (time or depth migrated domain).
In typical processing flows, a velocity model is conveniently available in the form of a stacking velocity estimate which may be derived during a “stacking” procedure in which seismic traces with common midpoints are corrected for differences in arrival times of corresponding reflection events to remove effects of different source receiver offsets used during acquisition (i.e. Normal move out). This stacking velocity is often taken to represent an RMS velocity. The stacking or RMS velocity differs significantly from the interval velocity. A particular difficulty with it is that the RMS velocity estimate for a particular interface at depth is a type of “average” of the velocities of the layers above the interface in question, such that there is a depth-dependent discrepancy between the RMS and interval velocity.
It is therefore sought to perform an inversion of the RMS velocity data to form an alternative velocity model that provides an improved estimate of velocity structure. This is often done by calculating Dix interval velocities using a well known relationship between the RMS velocities and the interval velocity of a given geological layer n sometimes called the Dix formula (Dix, C. H., 1955, Seismic velocities from surface measurements: Geophysics 20, 68-86):
                              V          n          2                =                                                            U                n                2                            ⁢                              t                n                                      -                                          U                                  n                  -                  1                                2                            ⁢                              t                                  n                  -                  1                                                                          Δ            ⁢                                                  ⁢                          t              n                                                          (                  Equation          ⁢                                          ⁢          1                )            
where
Vn is the interval velocity in layer n
Un is the RMS velocity at the bottom of layer n
Δtn is the two-way travel time across layer n
Further, it is well-known that the RMS velocity and the interval velocity are related to an instantaneous velocity function as defined by relationships:
                                          U            2                    ⁡                      (            t            )                          =                              1            t                    ⁢                                    ∫              0              t                        ⁢                                                            V                  2                                ⁡                                  (                  t                  )                                            ⁢                                                          ⁢                              ⅆ                t                                                                        (                  Equation          ⁢                                          ⁢          2                )                                          V          i          2                =                              1                          Δ              ⁢                                                          ⁢                              t                1                                              ⁢                                    ∫                              t                                  i                  -                  1                                                            t                i                                      ⁢                                                            V                  2                                ⁡                                  (                  t                  )                                            ⁢                                                          ⁢                              ⅆ                t                                                                        (                  Equation          ⁢                                          ⁢          3                )            
where
Vi is the Dix interval velocity in an interval between ti-1 and ti 
U(t) is the RMS velocity function
V(t) is the instantaneous velocity function
Δti is two-way travel time across the interval Δti=ti−ti-1 
In layers where the velocity is constant, the instantaneous velocity V(t) is the same as the interval velocity. Further, the Dix interval velocity Vi, as defined here, is a local RMS velocity. The relationships of Equations 1 to 3 can thus be used to “invert” the RMS velocities to obtain Dix interval velocities for the time interval between reflection events for which RMS velocities were determined.
The Dix interval velocities which are obtained using Equations 1 to 3 are dependent on the accuracy of the pre-estimated RMS velocities and correct identification of primary reflection events in the data. This can be problematic. The primary reflections are the events where the seismic wave has reflected only once at the geological horizon but there may also be present events where a seismic wave has reflected multiple times from interfaces and these events may interfere and obscure primary reflection events. There are also other sources of uncertainty. It can therefore be difficult for a data interpreter to identify the primary reflections and RMS velocities accurately. Therefore, the RMS velocity estimates are uncertain, which similarly may produce a source of uncertainty of the Dix interval velocities which are estimated from the RMS velocities.
In present techniques for inverting RMS velocity data to Dix interval velocities, uncertainty of this nature is not evaluated or taken into account, and therefore it can be difficult or impossible to assess the significance of the velocities calculated. Without an understanding of those uncertainties it is difficult to make use of the interval velocities, and any further results derived from them, in any quantitative way.
There are also significant limitations in the way that existing technologies take into account geological knowledge from the region. For example, a user may beforehand need to select parameters which affect the actual inversion algorithm such as damping in the inversion, honouring of the input data, and penalising deviation from a background velocity trend. Deciding the relative weighting of these parameters is not particularly intuitive with the result that the existing Dix inversion packages may be hard to use and, conversely, easy to misuse. Moreover, statistical uncertainties attached to the geological knowledge forming the basis for constraining an inversion are not accommodated.
Another limitation of known methods is that interval velocities are typically calculated for the particular intervals defined between high-amplitude reflection events of seismic reflection data. If the RMS velocities from different lateral locations are not available horizon-consistently, at each position for the same reflection event, the velocity data sets from one geographical position to another will be inconsistent, which may limit further applications of the data.